标题： 不可压缩密度变化的纳维-斯托克斯方程的人工可压缩性方法 显示英文标题

标题： Artificial compressibility method for the incompressible Navier-Stokes equations with variable density

摘要： 我们引入了一种新颖的人工可压缩技术，以近似具有可变流体性质（如密度和动力粘度）的不可压缩Navier-Stokes方程。 所提出的方案使用了压力和动量的耦合，等于密度乘以速度，作为主要未知数。 它还涉及对扩散算子的适当处理，使得显式处理非线性对流项可以得到一个时间独立刚度矩阵的方案，这适用于伪谱方法。 在假设密度通过一种保持最小-最大原理的方法进行近似的情况下，建立了该方案半隐式版本的稳定性和时间收敛性。 数值示例确认，在经典的CFL条件下，半隐式和显式方案都是稳定的，并且具有一阶收敛性。 此外，所提出的方案在涉及重力波和圆柱体内不混溶多流体的设置中，被证明比作者之前提出的一种基于动量的压力投影方法表现更好。 显示英文摘要

摘要： We introduce a novel artificial compressibility technique to approximate the incompressible Navier-Stokes equations with variable fluid properties such as density and dynamical viscosity. The proposed scheme used the couple pressure and momentum, equal to the density times the velocity, as primary unknowns. It also involves an adequate treatment of the diffusive operator such that treating the nonlinear convective term explicitly leads to a scheme with time independent stiffness matrices that is suitable for pseudo-spectral methods. The stability and temporal convergence of the semi-implicit version of the scheme is established under the hypothesis that the density is approximated with a method that conserves the minimum-maximum principle. Numerical illustrations confirm that both the semi-implicit and explicit scheme are stable and converge with order one under classic CFL condition. Moreover, the proposed scheme is shown to perform better than a momentum based pressure projection method, previously introduced by one of the authors, on setups involving gravitational waves and immiscible multi-fluids in a cylinder.